Bring the water to a boil in a saucepan. Stir in the grits. Cook for 8 minutes, stirring frequently. Add the cheese, stirring until melted. Stir in green chilies. Season with salt and pepper. Spoon the grits mixture into a greased 9x13 inch baking pan. Let stand until cool. Chill, covered, for 2 to 10 hours.
Cut the grits into 8 squares with oil. Cook on a hot griddle or in a large nonstick skillet until light brown and crisp on both sides.